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Tuesday, January 23, 2018

**Abstract:** Given a large point set in the plane, where is its 'center'? Unlike the 1-dimensional case, there is not a single answer. We will discuss some of these answers, with the focus on the result of Pach. He showed that one can always find three large subsets A,B,C and a 'central point' p such that every A-B-C triangle contains p. We will then explain the topological generalization of this and related results, where for example the triangle edges are no longer assumed to be straight. Based on a joint work with Alfredo Hubard.

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